The value of `x` for which the sixth term in the expansion of `[2^(log)2sqrt(9^(x-1)+7)+1/(2^(1/5)(log)_2(3^((x-1)+1)))]^7` is 84 is a. `4` b. `1or2` c. `0or1` d. `3`

Options

A. 4
B. 1 or 2
C. 0 or 1
D. 3

Answer

B

Explanation

By the given condition,
`84=T_(6)=T_(5+1)`
`=.^(7)C_(5)(2^(log_(2)sqrt(9^(x-1)+7)))^(2)((1)/(2^(1/5log_(2)(3^(r-1)+1))))^(5)`
`= 21 xx 2^(log_(2)(9^(x-1)7))2^(-log_(2)(3^(x-1)+1))`
or `4 = 2^(log_(2)'(9^(x-1)+7)/(3^(x-1)+1))=(9^(x-1)+7)/(3^(x-1)+7)`
or `(3^(x-1))^(2)-4xx3^(x-1)+3=0`
or `(3^(x-1)-1)(3^(x-1)-3)=0`
`rArr 3^(x-1)=1` or `3`
`rArr 3^(x-1)=3^(0)` or `3^(1)`
`rArr x-1 = 0` or 1
`rArr x = 1,2`